To test out the height ordering measure I came up with, and to try some of the methods described in recent posts on the Sabermetric Research blog, I decided to run some correlations to look at the relationship between a player’s height and his rebounding performance.

For the 2006-07 season, I looked at all players who played at least 200 minutes (which came out to 397 players, counting stints with different teams separately). I chose 200 minutes as the cutoff because the correlations seemed to stabilize at that level (at lower cutoffs the correlations were lower because of fluky low minute guys, and at higher cutoffs the correlations were very similar to what they were at the 200 minute cutoff). The explanatory variables that I used were height (in inches) and height ordering (which is on a 1 to 5 scale, with 1 indicating that the player played all of his minutes as the shortest player on the court for his team). The response variables were defensive rebounding percentage and offensive rebounding percentage. DRB% is an opportunity rate measuring DRB/(DRB opportunities), or more specifically, DRB/(team DRB while the player was on the court + opponent ORB while the player was on the court). ORB% is similar but uses ORB opportunities. The actual formulas, which estimate the on-court part, are as follows:

DRB% = DRB/((5*MIN/tmMIN)*(tmDRB + oppORB))
ORB% = ORB/((5*MIN/tmMIN)*(tmORB + oppDRB))

Last season, among players who played at least 200 minutes, Kevin Garnett led the league in DRB% at 30.7%. Earl Boykins finished last at 5.1% for his stint in Denver. For ORB%, Justin Williams was first at 17.6%, while Keith McLeod was last at 0.3%.

Correlations and Regression Equations

Correlation coefficients (r):

       DRB%  ORB%
       ----  ----
Ht      .68   .73
HtOrd   .75   .76

Regression equations (Y = mX + b):

DRB% = 0.007*Ht + -0.49 or
DRB% = 0.7%*(Ht - 71)

ORB% = 0.011*Ht + -0.73 or
ORB% = 1.1%*(Ht - 66)

DRB% = 0.021*HtOrd + -0.007 or
DRB% = 2.1%*(HtOrd - 0.3)

ORB% = 0.032*HtOrd + 0.046 or
ORB% = 3.2%*(HtOrd + 1.45)

So for each additional inch of height, the average player gained 0.7% in his DRB% and 1.1% in his ORB%.

And for each additional unit of height ordering (i.e. moving up from 1st shortest to 2nd shortest, or 3rd to 4th, etc.), the average player gained 2.1% in his DRB% and 3.2% in his ORB%.

Analysis

Let’s go back to the correlation coefficients. The first thing to notice is that they are all pretty high. An r of around .7 means an r-squared around .5, which indicates that height accounts for around 50% of the variance in rebounding percentages. Whatever other factors contribute to rebounding, none will have the impact that height does.

The next thing I noticed was that for both offensive and defensive rebounding, height ordering correlated better than just plain height. This provides some evidence that the height ordering measure I came up with is picking up some important information that can’t be gained just by looking at height.

Interestingly, offensive rebounding seems to be determined by height more than defensive rebounding (.73 to .68), but this difference almost completely disappears when we look at height ordering (.76 to .75). I’d have to take a closer look to really figure out what’s going on there, but I have some initial speculation. My guess is that height ordering correlates better to DRB% than height mainly because of undersized big men who grab more defensive boards than the typical player their height simply because they are playing a position that puts them closer to the hoop on defense. In other words, a 6′8″ player who is forced to play most of his minutes as the second tallest player on the court for his team (i.e. at a height ordering of 4), will be guarding opposing PFs close to the hoop, and thus be in a better position for defensive rebounds than the typical 6′8″ player, who is guarding SFs on the perimeter (and who has a height ordering of 3).

That’s all I have for now, though I think there are a lot of interesting directions one could go in using this as a starting point. For instance, what are the implications of the fact that a huge factor in rebounding is an aspect of a player that is completely unchanging regardless of team context, coaching, player improvement, aging, etc. (though note that while height is fixed, height ordering is not)? And should we account for player height or position in evaluating rebounding, either on its own or as part of a more comprehensive metric?

Here are a few more interesting correlations that I’ll post without analysis:

Offensive Rebounding Percentage & Defensive Rebounding Percentage:

      DRB%
      ----
ORB%   .77

Block Percentage [BLK/((5*MIN/tmMIN)*opp2PA)] & Height:

       BLK%
       ----
Ht      .62
HtOrd   .66